The pairing mechanism in high temperature cuprate superconductors is an interesting problem. A low energy effective theory called spin-fermion model can be applied to study cuprates, and it's argued that pairing in cuprates is mediated by spin fluctuations. The model describes low-energy fermions interacting with their own collective spin fluctuations.

For phonon mediated superconductors, vertex corrections of phonon electron interactions and momentum dependence of fermionic self energy are small and neglected, due to the small ratio of sound velocity and Fermi velocity. This leads to the well known Eliashberg equations for superconducting state. For cuprates, Eliashberg-type theory is still valid, but for different reasons with phonon mediated superconductors, in spite of strong spin fermion interactions. Many 'fingerprints' of the spin fluctuation mediated pairing mechanism has been seen in the experiments.

This is the first talk of two consecutive Journal Club talks using spin-fermion model to study cuprates. I will focus on:
1.Introduction to spin-fermion model.
2.Summary of Eliashberg theory for electron-phonon pairing.
3.Perturbation theory and Eliashberg-type equations for spin fermion model.
4.Two of the fingerprints: Comparison with ARPES and neutron scattering experiments for superconducting state.